How do I 'switch' to another countries store so I can update my apps?

Hi, my iPhone 5 was set up in NZ along with my iTunes account. All of my current apps have been purchased from the NZ store. We have moved to Hong Kong and I now wish to update my apps but am being told:

Account not in this store.

Your account is not valid for use in the HK store. You must switch to the NZ store before purchasing.

Button Option on screen; Cancel or Change Store

When I select Change Store on my iphone the screen just goes blank and then says 'Done' with nothing generated on the screen.

Qu - do I need to do something to my iphone before selecting 'Change Store' so it actually takes me when I need to be OR do I access the Change Store functionality on my iTunes account and then sync my iphone?

Thank you!!